SOLUTION: An airplane is flying east at a constant altitude of 28,000 meters. The pilot spots a ship at an angle of depression of 18.5 degrees . After 73 seconds the angle of depression is

Question 1199944: An airplane is flying east at a constant altitude of 28,000 meters. The pilot spots a ship at an angle of
depression of 18.5 degrees . After 73 seconds the angle of depression is 38.4 Degrees. Find the speed of the plane.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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An airplane is flying east at a constant altitude of 28,000 meters.
The pilot spots a ship at an angle of depression of 18.5 degrees.
After 73 seconds the angle of depression is 38.4 Degrees.
Find the speed of the plane.
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For the angle of 18.5°,  tan(18.5°) = ,

where    is the first horizontal diatance, measured at the sea level.

So,   =  =  = 83682 meters.



For the angle of 38.4°,  tan(38.4°) = ,

where    is the second horizontal diatance, measured at the sea level.

So,   =  =  = 35327 meters.


Thus, in 73 seconds, the airplane covered  83682 - 35327 = 48355 meters.


Hence, the speed of the airplane is   = 662.397 m/s = 2384 km/h.    ANSWER

Solved.

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To which direction the airplane is flying (east, west, north, south), it does not matter.

What does really matter in this problem, is that the pilot sees the ship straight ahead.

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